Question

Giải phương trình:

a) \(\sqrt[4]{x+8}\)+\(\sqrt[4]{x-7}\)=3

Answer 1

ĐKXĐ: \(x\ge7\)

Đặt \(\left\{{}\begin{matrix}\sqrt[4]{x+8}=a>0\\\sqrt[4]{x-7}=b\ge0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}a+b=3\\a^4-b^4=15\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}b=3-a\\a^4-b^4=15\end{matrix}\right.\)

\(\Rightarrow a^4-\left(3-a\right)^4=15\)

\(\Leftrightarrow2a^3-9a^2+18a-16=0\)

\(\Leftrightarrow\left(a-2\right)\left(2a^2-5a+8\right)=0\)

\(\Leftrightarrow a=2\)

\(\Leftrightarrow x=8\)